THE PERSISTENCE OF EARLY CHILDHOOD MATURITY:
INTERNATIONAL EVIDENCE OF LONG-RUN AGE EFFECTS*
Kelly Bedard and Elizabeth Dhuey
Abstract
A continuum of ages exists at school entry due to the use of a single school cut-off date – making
the “oldest” children approximately twenty percent older than the “youngest” children. We
provide substantial evidence that these initial maturity differences have long lasting effects on
student performance across OECD countries. In particular, the youngest members of each cohort
score 4-12 percentiles lower than the oldest members in grade four and 2-9 percentiles lower in
grade eight. In fact, data from Canada and the United States shows that the youngest members
of each cohort are even less likely to attend university.
*We thank the conference participants at the CIBC Conference on Human Capital and Productivity at the University
of Western Ontario and the 2005 Society of Labor Economists Meetings in San Francisco, seminar participants at
UC Irvine, UC Davis, and UC Santa Barbara, and particularly David Blau, John Bound, Elizabeth Cascio, Peter
Kuhn, Kevin Lang, Marianne Page, Jeff Smith, Jon Sonstelie, and Lawrence Katz and three anonymous referees for
helpful comments.
I. INTRODUCTION
Nearly all education systems have a single cut-off date for school eligibility. For
example, a child may be allowed to enter kindergarten as long as he is five years old by
September 1 of the relevant year. Cut-off dates are important because they cause some students
to be older than others when they begin school. To put this in perspective, in an education
system in which students must be five to start school, the oldest students are approximately
twenty percent older than the youngest students at school entry. Given the magnitude of the age
range on the first day of school, the oldest students are likely to be substantially more mature
than the youngest students. As such, one would expect an age-based performance differential
during the early grades. If this relative maturity effect is significant in early primary grades, but
then dissipates with age, this phenomenon, while interesting, is not particularly important for the
economy. On the other hand, if early relative maturity effects propagate themselves through the
human capital accumulation process into later life, long after small differences in age are
important in and of themselves, they may have important implications for adult outcomes and
productivity.
Recent work by Heckman and various coauthors (see Cuhna, Heckman, Lochner, and
Masterov [2006] for an excellent review) argues that skills accumulated in early childhood are
complementary to later learning. Relative age differences at the start of formal schooling may
therefore be long-lasting if relatively older students are better positioned to accumulate more
skills in the early grades because their maturity advantage increases the likelihood that they are
selected for more advanced curriculum groups or because they progress through a common
curriculum at a faster rate.1 Notice that relative age effects can persist either because students
are separated into programs with different rates of human capital accumulation during the early
1
primary grades or because stronger students are encouraged to continue progressing through the
curriculum while weaker students are simply allowed to lag farther and farther behind. As such,
relative age effects can be generated by education systems using ability-specific curriculum
groups during the primary grades like in England and the United States as well as by countries
that employ social promotion and claim to have no ability specific tracking, such as Japan.
Uncovering the causal impact of early relative maturity on later outcomes is difficult
because age enters into educational decisions in at least four important ways. First, school cutoff dates only determine relative age if the rules are strictly followed. For example, a significant
fraction of American children defer school entry by a year, making them the oldest students
[Datar, 2006]. This is problematic because these children are not a random draw. To distinguish
between observed relative age and the relative age at which a child should be observed, based on
their birth date relative to the school cut-off date, we refer to the latter measure as assigned
relative age. Secondly, children who are young at school entry are more likely to repeat a grade.
Thirdly, relative maturity may at least partially determine academic program placement during
elementary school. Finally, at young ages, relatively older students will be more mature and
hence score higher on achievement tests, independent of program placement.
While relative age evaluated at any point in the educational process is endogenous, the
initial timing of births is arguably exogenous. We therefore compare the test scores of children
with older and younger assigned relative ages at the fourth and eighth grade levels across OECD
countries using data from the Trends in International Mathematics and Science Study (TIMSS).
Following from the previous discussion, the impact of assigned relative age on test scores
reflects both differential school entry and grade retention/failure across the assigned relative age
distribution, as well as differences in program placement and skill acquisition, and is therefore a
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net, or reduced form, effect. Given that we know both observed and assigned relative age, we
can also estimate the causal (within grade) impact of relative age using assigned relative age as
an instrument for observed age. Finally, since some of the countries participating in TIMSS
employ “clean” education systems, in the sense that essentially all children enter on time and
pass from one grade to the next on schedule, we can also compare the clean countries to the rest
of the countries to get a sense of the relative importance of failure and within grade differences
in relative maturity in determining the net (reduced form) relative age effects. Our ability to
compare countries with different education systems in TIMSS is one of the important novelties
of this paper. Using the data from nineteen countries allows us to ascertain the pervasiveness of
relative age effects across countries and education systems.
Overall, we find that the youngest students score substantially lower than the oldest
students at both the fourth and eighth grade levels. In grade four, the youngest students score
1.2-3.5 points lower on nationally standardized tests with a mean of 50 and a standard deviation
of 10. To put this in perspective, this translates into a 4-12 percentile disadvantage for eleven
months of relative age. While the age premium enjoyed by the oldest students declines between
grades four and eight, there remains a 0.8-2.6 point difference, or 2-9 percentiles, between the
oldest and the youngest students at the eighth grade level. These results clearly show the
persistence of relative age into adolescence, and are therefore suggestive of a longer run impact.
In order to confirm the existence of long-run relative age effects, the last section of the
paper examines the impact of relative maturity on the probability of participating in a preuniversity program during the final year of high school in British Columbia, Canada and the
probability of writing the SAT and enrolling in an accredited four year college in the United
States – the only two jurisdictions for which we have been able to obtain micro-level university-
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stream and month of birth data. In British Columbia, individuals born in the relatively youngest
month are underrepresented in the pre-university program by 9.8 percent. The results for the
United States are similar: Individuals born in the first assigned relative month are
underrepresented in the pre-university stream (as measured by taking the SAT or ACT) by 7.7
percent. Further, individuals born in the first relative month are underrepresented in accredited
four-year college/universities enrollments by 11.6 percent. Taken as a whole, the results from
TIMSS and the university-bound/enrollment results from British Columbia and the United States
clearly point to substantial long-run relative age effects that have important implications for the
distribution of adult skills.
The remainder of the paper is as follows. Section II discusses the possible avenues
through which relative maturity may be propagated into adulthood. Section III describes the
econometric framework. Section IV discusses the data used in the analysis and looks for birth
date targeting. Section V reports the relative age estimates at the fourth and eighth grade levels.
Section VI analyzes the impact of relative age on pre-university program and college enrollment.
Section VII concludes.
II. THE PROPAGATION OF EARLY MATURITY DIFFERENCES
INTO THE LONG-RUN
Despite the myriad of educational structures used across countries, essentially all nations
have two common features: (1) A single annual cut-off date,2 which generates at least a one-year
age range within each grade cohort and (2) Ability-based sorting into curriculum groups or
classes. In some countries sorting takes the form of strict program based streaming (i.e.
academic versus vocational) while in others it takes the more flexible form of ability grouping
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(i.e. reading groups). In fact, even countries that employ social promotion (automatic promotion
from one grade to the next) and claim to have only one track are implicitly streaming to the
extent that the weakest students are allowed to fall progressively farther behind. These types of
educational structures are importantly related to relative age because skill-based curriculum
usually begins during the primary grades when relative maturity likely plays a large part in
determining skill differences between young and old students. The interaction between the
timing of skill-based curriculum commencement and relative maturity may therefore play a
central role in determining program/group placement, and may hence affect skill accumulation
throughout the educational process, even after relative age is irrelevant in and of itself.
Allen and Barnsley [1993] provide us with a simple example. They report that 72 percent
of boys between the ages of 16-20 playing in the highest level of minor hockey in Canada are
born in the first half of the year (the cut-off date for Canadian hockey is January 1). This results
because the substantial variation in maturity within young cohorts makes it more likely that older
boys are selected for more competitive (rep) teams. Since rep teams attract the best coaches,
practice more, and play against higher caliber opponents, rep team members accumulate more
hockey skills and thereby increase their probability of being selected for rep teams in the future.
While it would be surprising to find such enormous relative age differences for long-run
educational outcomes, the combination of the Allen and Barnsley results and the extensive use of
skill-based curriculum in schools (see Appendix Table I) certainly suggest that there is the
potential for substantial differences in educational success across the relative age distribution.
Given the discussion so far, it is tempting to hypothesize that countries that rigidly stream
students into academic and vocational streams at young ages will have the strongest propagation
of relative age effects into adolescence and adulthood. This is particularly appealing since this
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type of streaming is observable and hence seems testable. However, this type of streaming does
not usually occur until adolescence, long after less rigid forms of streaming such as reading and
math groups and enrichment programs have already begun. As such, adolescent stream
placement is at least partly an outcome of early maturity differences that influence primary level
program placement and subsequent academic progress. Since most countries use such structures,
it is difficult to determine, a priori, which countries we should expect to have the largest relative
age effects. Further, there will even be relative age differences in student performance in
countries that use social promotion as long as stronger students are encouraged to continue
moving ahead even as weaker students fall behind. This is of course what one would expect
unless students are only allowed to accumulate a specific set of skills in each grade and are then
forced to wait for the rest of the class to catch up before progressing.
III. ECONOMETRIC FRAMEWORK
We begin with a simple model of the relationship between student outcomes and
observed age.
(1) Scgi = α cg + β cg Acgi + X cgi γ cg + ε cgi
where Scgi denotes student outcomes, usually a test score, for student i in country c in grade g, A
is observed age, X is the vector of controls described in Section IV, and ε is the usual error term.
All models are estimated separately for each grade and country. The parameter of interest is β cg
– the causal impact of relative age. However, the causal interpretation rests on the assumption
that unobservables do not confound the observed age effect, which is clearly untrue given nonrandom grade retention. Since children who enter kindergarten early tend to score worse than
they otherwise would and there are many more children who are old because they are retained
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(who tend to score poorly) than children who are old because their parents hold them out of
school so that they enter kindergarten a year late (who are positively selected), OLS estimates are
downward biased. In fact, in countries where a large fraction of students repeat at least one
primary grade, such as in the United States, the OLS estimates can even be negative (see Section
V).
We propose an instrumental variables (IV) solution to this problem using birth month
relative to the school cut-off date, assigned relative age (R), as an exogenous determinant of
observed age. More specifically, we estimate the parameters of equation (1) using TSLS based
on the following the first-stage equation for observed age:
(2) Acgi = π 1cg + π 2 cg Rcgi + X cgi π 3cg + vcgi .
While the reduced form relationship between observed age and assigned relative age (the
first stage) is not particularly interesting, the reduced form relationship between test scores and
assigned relative age is important from a policy perspective.
(3) Scgi = θ1cg + θ 2 cg Rcgi + X cgiθ 3cg + ucgi
In particular, θ 2cg measures the impact of assigned relative age net of grade repetition and late
entry. Stated somewhat differently, θ 2cg is the overall, net, or reduced form impact of assigned
age on test scores at a given grade level g (we return to this point in Section V.A).
For the IV estimator to provide a consistent estimate two conditions must be satisfied.
First, assigned relative age must be correlated with observed relative age. Since most students
enter school on time and are never retained this is easily satisfied (see Tables III and IV). In
other words, assigned relative age is clearly an important determinant of observed age. The
second condition requires that assigned relative age be uncorrelated with the unobserved
determinants of test scores. This assumption is violated if, for example, children born at
7
different times of the year have higher or lower unobserved ability levels. We explore this issue
in two ways. First, we study birth month patterns to check for birth date targeting by different
socioeconomic groups (see Section IV.D). Secondly, we control for season of birth effects
directly by estimating an alternative specification that includes both assigned relative age and
month of birth using data pooled across countries with cut-off dates in different months (see
Appendix Table I).3 For example, the school cut-off date is September 1 in England, January 1
in France, and April 1 in Greece. As such, children born in the same calendar month (season of
birth) have different relative ages if they live in different countries. This is helpful because it
make us more confident that we are not confounding season of birth and relative age (see Bound
and Jaeger [2000]).
For concreteness, the main equation becomes,
(4) Scgi = ϕ1cg + ϕ 2 g + ϕ 3 g Acgi + X cgi ϕ 4 g + ν cgi
where Scgi is an internationally standardized test score, ϕ1cg is a vector of country indicators, and
ϕ 2 g is a vector of month of birth indicators (to capture season of birth effects that are common
across countries). Unlike equation (1), this TSLS model is estimated using data pooled across
countries, but separately by grade.
Our ability to separate the effects of relative age and season of birth using test data across
countries with different school start dates is one of the unique features of this study. While we
are not the only economists to have examined the impact of relative age on student performance,
ours is the only study capable of separating relative age and season of birth. This is due to the
fact that recent work by Datar [2006] for the United States, Fredriksson and Öckert [2004] for
Sweden, and Puhani and Weber [2005] for Germany are all based on samples from a single
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country with a single school cut-off date, or in the case of the United States almost all fall/early
winter cut-off dates.4
IV. DATA
The data used in this study come from five sources. Our primary sources are the 1995
and 1999 Trends in International Mathematics and Science Study (TIMSS), which we
supplement with the Early Childhood Longitudinal Study (ECLS) and the National Education
Longitudinal Study (NELS) data for the United States in order to examine fourth and eighth
grade test scores. In addition, we also use administrative data for British Columbia, Canada and
NELS data for the United States to estimate the long-run impact of relative age on pre-university
program and college participation. To avoid confusion, this section focuses on our primary
(TIMSS) and supplementary (ECLS and NELS) data sources. The secondary data sets used to
examine university outcomes are described in Section VI.
IV.A. The Trends in International Mathematics and Science Study (TIMSS)
TIMSS is an excellent source for studying the impact of relative age on student
performance it includes nationally representative mathematics and science achievement results
for third and fourth graders in 26 countries in 1995 and seventh and eighth graders in 41 and 38
countries in 1995 and 1999, respectively. We restrict the sample to OECD countries with
unambiguous nationwide school starting age rules (cut-off dates). Australia, Germany, Hungary,
Ireland, the Netherlands, Switzerland, and the United States are excluded because their rules
regarding the school cut-off date either differ across regions, which are not reported in TIMSS,
or the cut-off date is at the discretion of educators and/or parents. In addition, Korea and Turkey
are excluded because their birth date data is of questionable quality.5 These exclusions leave us
9
with a sample of 10 countries for third and fourth graders and 18 countries for seventh and eighth
graders: For a total of 228,629 observations across all ages and countries. However, students
who do not report their sex, birth month, birth year, test year, or test month are excluded,
reducing the sample by 2,857 students. The country-grade specific sample sizes are reported in
Table I.
It is important to clarify exactly who is being tested. The 1995 TIMSS includes test
scores for two different grade groups. The first set of scores is for students enrolled in the two
adjacent grades that contain the largest proportion of nine-year-olds – third and fourth graders in
most countries. For expositional ease, we refer to these students as fourth graders. The second
set of scores is for students enrolled in the two adjacent grades that contain the largest proportion
of thirteen-year-olds – seventh and eighth graders in most countries.6 We refer to these students
as eighth graders. In contrast, the 1999 TIMSS includes only one age group in a single grade.
While the 1999 TIMSS uses the 1995 definition to target the two adjacent grades containing the
most thirteen-year-olds, only students in the upper of the two grades were tested – eighth graders
in most countries. We again refer to these students as eighth graders.
The TIMSS test scores used in all analyses are standardized to mean 50 and a standard
deviation 10. Two distinct standardizations are used. First, all country specific models are
estimated using test scores that are standardized by test book within each country. Within test
book standardization is required because each student wrote only one of eight possible exams,
and within country standardization allows us to include United States estimates based on ECLS
and NELS data in Tables III and IV.7 Second, the cross-country models use data that is
standardized within test book across all TIMSS participants. In both cases, the data is population
weighted. Summary statistics for the internationally standardized scores are reported in Table I
10
by country. As one would expect, the country-specific internationally standardized scores means
are generally above 50 because we are focusing on the subset of OECD countries. We do not
report the within country standardized scores since the means and standard deviations only differ
from 50 and 10 due to a small number of sample exclusions necessitated by missing data.
Measuring assigned relative age requires knowledge of the cut-off date for children to
begin school. For example, if a child is allowed to enter kindergarten as long as he has reached
the age of five by September 1 of the relevant year, then September 1 is the cut-off date. We
determined these cut-off dates using the empirical distribution of birth months in each country.
The beginning of the first month of the twelve consecutive months that contains the largest
percentage of student birth dates is defined as the cut-off date. We then confirmed each of these
dates using Eurydice (see www.eurodice.org), an information network on education in Europe,
established by the European Commission, or by using an individual country’s Department of
Education website. We then use the cut-off date and month of birth, which is reported in
TIMSS, to construct a linear measure of assigned relative age (R). More specifically, R = 0 for
students born in the last eligible month and R = 11 for students born the first eligible month. For
example, if the cut-off date is January 1, December babies are the youngest (R = 0) and January
babies are the oldest (R = 11). Actual age in months (A) is constructed using the test date and
birth date, both of which are reported in months.
All test score models include a basic set of socio-economic controls. These include
indicator variables for sex, grade, test year (in eighth grade models only), rural residential
locations, native born mother, native born father, child living with both parents, child has a
calculator, child has a computer, child has more than 100 books, and parental education (in
eighth grade models only), and a continuous measure for the number of people residing in the
11
child’s household. Unfortunately, there is a fair amount of non-reporting for some of the
socioeconomic controls, and as we do not want to lose observations due to missing
socioeconomic information, we replace the missing control variable observations with zeros and
include a set of dummy variable indicating missing data.8 It is also important to point out that
the grade dummy captures both across grade learning and absolute age. Accordingly, these two
effects cannot be statistically separated in this framework.9
IV.B. ECLS Data for 3rd Grade
As explained in the previous sub-section, the TIMSS data for the United States are not
usable because it does not include state of residence. We therefore use the ECLS to examine the
impact of relative age on math and science test scores in the United States. However, one
drawback of the ECLS is that the sampling frame is different from the TIMSS sampling
structure. Where TIMSS test scores are for a particular grade, the ECLS test scores are for a
particular age. More specifically, the ECLS sample includes children enrolled in kindergarten in
1998. The ECLS then tracks these children through 2002, at which time most children are in
grade three, but children who have failed a grade are in grade two (7.27 percent of the sample),
and children who have failed two grades are in grade one (0.03 percent of the sample). In order
to make the ECLS and TIMSS samples as similar as possible, we restrict the sample to children
who entered kindergarten for the first time in 1998 for whom we have complete information
regarding sex, birth date, school cut-off date, school year start date, test scores, race, number of
siblings, rural status, parental education, whether the child lives with both mother and father,
owns over 100 books, and owns a calculator. This leaves us with 6,091 observations. Finally, to
make to ECLS results as comparable as possible to the TIMSS results, the math and science
scores are standardized to have a mean of 50 and a standard deviation of 10.
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IV.C. NELS Data for 8th Grade
Since the available ECLS waves currently end at grade three, we turn to NELS to
examine the impact of relative age on academic achievement at the eighth grade level. NELS is
a nationally representative sample of eighth-graders who were first surveyed in the spring of
1988. Unlike the ECLS, the NELS sample structure is identical to the TIMSS sample structure.
We restrict the sample to students with complete test score, birth date, sex, race, family size,
living with both mother and father, urban, owning over 50 books, owning a calculator, and
parental education data. We further restrict the sample to states in which there exists a single
precisely defined school cut-off date during the sample period.10 Finally, states with a midmonth cut-off are also excluded since we know the month of birth but not the day of birth. This
leaves us with 15,155 observations. Again, to make the NELS and TIMSS estimates as
comparable as possible, the math and science scores are standardized to have a mean of 50 and
standard deviation of 10.
IV.D. Is Assigned Relative Age Random or Do Some Parents Target “Old” Relative Ages?
Before proceeding to the results section of the paper, it is important to examine the
potential endogeneity of relative age due to parental birth date targeting aimed at ensuring that
their child is the oldest in their class. To investigate this possibility, Table II reports the fraction
of children in TIMSS (years and age groups are combined) born in each calendar and school
quarter. Focusing first on the calendar quarter of birth, i.e. January – March is quarter 1 and
October – December is quarter 4, it is clear that births are evenly distributed across calendar
quarters. Further, to the extent that any quarter is slightly favored, it is either 2 or 3 (spring or
summer).
13
More interesting for our purposes are the relative school age patterns. While it might
seem that we could detect birth date targeting by looking for elevated birth rates in the fourth
school quarter, this is not possible due to the mild seasonality in birth patterns shown in the first
four columns of Table II. Even mild seasonality makes detecting birth date targeting difficult, or
impossible, because strictly speaking we expect parents who target to have a somewhat higher
fourth school quarter birth rate than parents who do not target age at school entry.
The last four columns of Table II therefore explores the possibility that more educated
mothers may target their child’s birth date more than less educated mothers. More specifically,
these columns report the difference in the percentage of children born in each relative quarter for
more and less educated mothers. These results are based on the eighth grade sample because
maternal education is not reported for fourth graders. More educated mothers are defined as
those with education levels in the top 30-40 percent of the education distribution within their
country.11 Japan and England are excluded because they do not report maternal education
information. The results reported in columns 9-12 reveal only a few (7 out of 60) statistically
significant differences across maternal education groups. Further, the significant differences that
do exist provide no support for the hypothesis that mothers that are more educated target birth
dates in order to ensure that their children are the oldest in their class. In fact, if there is a
pattern, albeit a very weak one, it is that more educated mothers are slightly more likely to target
the first relative age quarter in many countries. A possible explanation for this pattern is that a
small fraction of more educated mothers target summer birth dates, likely for work reasons.12
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V. THE IMPACT OF RELATIVE AGE ON TEST SCORES
V.A. Grade 4
We begin the analysis by focusing on individual countries at the fourth grade level.
Table III reports the results for all equations of interest for mathematics (columns 1-4) and
science (columns 5-8). For comparative purposes, columns 1 and 5 report the OLS results for
the impact of observed age on test scores, equation (1). Columns 2 and 6 (labeled RF) and 3 and
7 (labeled FS) report the reduced form and first stage estimates for θ 2 gc and π 2cg , equations (3)
and (2), respectively. Lastly, columns 4 and 8 report the IV estimates for β cg using assigned
relative age as an instrument for observed age.
It is easiest to begin with the four countries for which there is little or no evidence of
early/late starting or grade retention: England, Iceland, Japan, and Norway (these countries are
shaded). For these countries, there are no, or at least very few, confounding factors to contend
with when estimating relative age effects as essentially all children follow the entry rules and
progress on time. Stated somewhat more formally, since the mapping from assigned relative age
to observed age is almost exact for these countries, the reduced form estimate ( θ 2 gc ) and the IV
estimate ( β gc ) should be almost identical. Comparing columns 2 and 4 (or 6 and 8) shows this to
be the case. More interestingly, the point estimates for the impact of relative age are large for all
countries. Referring to IV estimates reported in column 4, one month of additional relative age
increases the average math test score by 0.330, 0.258, 0.291, and 0.255 in England, Iceland,
Japan, and Norway, respectively. These coefficients translate into average math test score
premiums for the relatively oldest (R=11) compared to the relatively youngest (R=0) of 3.6, 2.8,
3.2, and 2.8 points on a standardized test with a mean of 50 and a standard deviation of 10. To
put these numbers into perspective, they imply 12, 11, 12, and 11 percentile test score ranking
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premiums for eleven months of relative age, for the respective countries – a massive advantage
by any metric (see Figure I). The reduced form percentile premium is the difference between the
mean predicted percentile evaluated at R=11 and the mean predicted percentile evaluated at R=0,
where the predicted percentiles are based on the empirical country-grade specific test score
distributions. The IV age premium is analogously defined, except that R=11 is replaced by
A=oldest on-time age and R=0 is replaced by A=youngest on-time age.
The remaining (not shaded) countries in Table III all have a sizeable minority of students
either ahead or, more likely, behind their assigned grade at the time of testing (see Appendix
Table I). Further, students who are behind are more likely to be relatively young and those who
are ahead of their assigned grade are more likely to be relatively old.13 As such, assigned
relative age also affects test scores through grade acceleration and retention/late entry. While it
is impossible to distinguish between late entry and retention in TIMSS, evidence from the ECLS
in the United States shows that by grade three, 12.2 percent of children are behind and that 40.6
percent of this fraction is due to late entry and 59.4 percent is due to retention. In contrast, if we
restrict attention to the relatively youngest children in the United States (R=0), 41.4 percent of
children are behind and that 57.4 percent of this fraction is due to late entry and 42.6 percent is
due to retention. These percentages clearly show that the relatively youngest children are both
more likely to be held back by their parents and more likely to repeat a grade during primary
school, at least in the United States.
While there is substantial variation in the amount of retention and acceleration across
countries, there is a common pattern across assigned relative ages: Younger children are more
likely to be behind their assigned grade and older children are more likely to be ahead of their
assigned grade. As such, the results reported in Table III are the overall, or net, impact of
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assigned relative age on test scores. They are net in the sense that children who have been
retained have had an extra year of education at the time of the test, and their score includes this
investment. Accordingly, as relatively younger children are more likely to be retained, relative
age affects test scores both through within grade differences as well as through retention. Note
that the reverse is not generally true for those who have been accelerated. As most acceleration
occurs at school entry, these children are younger, and hence may score worse as a result, but
they have not lost a year of training. The reduced form estimates are important from a policy
perspective because they measure the impact of relative age at a specific grade and therefore
incorporate both within grade differences in age and retention differences across relative ages.
In other words, if retention is partly determined by relative age, and if retention is effective at
raising human capital, then the reduced form relative age effects estimates should be smaller than
the IV estimates because the latter exclude the impact of retention since the age of children
observed ahead or behind their assigned grade cannot be predicted by assigned relative age.
Several features of Table III warrant comment. First, as discussed in Section III, the OLS
estimates are substantially downward biased in countries with high behind rates because children
who are old due to retention (who tend to score poorly) substantially out number children whose
parents hold them out of school so that they enter kindergarten a year late (who are positively
selected). The exception is the United States, which has a strong positive OLS estimate despite a
reasonably high behind rate. This reflects the difference in the sampling frame. In the ECLS,
students are observed in the spring of their fourth year of school regardless of grade. As such,
observed young students – who are the most likely to be retained – score poorly both because
they are young and because they have not yet completed as much curriculum and the small
number of observed old students whose parents entered them into kindergarten a year late tend to
17
be positively selected and hence score highly. Second, all of the reduced form and IV estimates
are statistically significant at the conventional level. Third, in all but the “clean” countries, the
IV estimates are larger than the reduced form estimates, although in some cases the difference is
not statistically significant. These findings suggest that retention may partly ameliorate the
disadvantage of being relatively young, at least in some countries, and at least in terms of test
scores at the fourth grade level.14 Fourth, and most importantly, the size of the relative age
premium is large in all countries at the fourth grade level. Finally, the Table III results are
consistent with the Puhani and Weber [2005] estimates showing that relatively old German
students score 0.4 of a standard deviation higher on the Progress in International Reading
Literacy Study (PIRLS) exam at the end of grade four.15
In order to more easily describe the magnitude of the relative age premium, panel A in
Figure I graphs the reduced form and IV estimates of the math test score percentile premium for
the oldest students (R=11) compared to the youngest students (R=0). There are two general
groups – countries with low failure rates and countries with high failure rates. In general, the
low failure rate countries (England, Iceland, Japan, and Norway) have large relative age effects,
with similar reduced form and IV estimates. For these countries, the oldest children score 11-12
percentiles higher than the youngest children. Among the high failure rate countries the pattern
is quite different: The reduced form estimates are smaller than the IV estimates and the relative
age effects tend to be somewhat smaller than in the low failure rate countries. The IV point
estimates generally range from a 2-3 point advantage (6-10 percentiles) for the oldest children
and a reduced form point estimate advantage generally ranging from 1-2 points (4-8 percentiles).
The one anomaly is New Zealand. The IV estimate for New Zealand is extremely large; a 4.7point (17 percentile) advantage for the oldest children, but the reduced form estimate is only 2.2
18
(an 8 percentile difference) – by far the biggest differential between the two estimates. The
anomaly is that the behind rate in New Zealand is only 7 percent. However, New Zealand has a
high acceleration rate, 5 percent, which is likely driving the large difference in the two estimates.
V.B. Grade 8
As discussed in Section I, our primary objective is to estimate the persistence of relative
age effects. While one might expect a few months of relative maturity to impact performance
during the primary grades, it is less clear how important this might be at older ages. Its
magnitude depends on the interaction of relative age and the structure of the education system,
the degree to which human capital accumulated in early childhood is complementary to later
human capital accumulation, and the extent to which young students and their teachers exert
additional effort to bring the achievement of young students up to that of their older peers.
Table IV replicates Table III for the eighth grade sample. The main finding for the eighth
grade sample is that relative age continues to be an important determinant of test scores even at
the end of middle school and the beginning of secondary school. In general, the IV point
estimates range from approximately 0.13 to 0.38, which is consistent with the statistically
significant positive secondary school results reported by Fredriksson and Öckert [2004] for
Sweden. Unlike the fourth grade sample, a few of the coefficient estimates are statistically
insignificant. In particular, there is no evidence of relative age effects in Denmark or Finland.
However, one should expect weak relative age effects in countries where formal curriculumbased education begins later because initial age differences will be less important. In contrast to
almost all other countries in the sample, compulsory education does not begin until age seven in
Finland and even then, the initial grades emphasize play and personal development rather than
curriculum-based activities. And in Denmark, differentiation on the basis of ability is officially
19
prohibited before the age of sixteen [OFSTED 2003]. Given these educational features, it is not
be surprising that we fail to find relative age effects in these countries.
The other substantive difference between Tables III and IV is that the United States
sampling frame in NELS matches that of TIMSS. As such, all United States point estimates
reported in Table IV are comparable to those of other countries. As one would expect, the
United States OLS estimates are now negative, the reduced form and IV estimates are now
similar to the Canadian estimates, and the gap between the reduced form and IV estimate is fairly
large. Based on the reduced form (IV) coefficient, the relatively oldest United States students
score 1.1 (2.6) points higher in mathematics than the relatively youngest students, or 4 (8)
percentiles higher.
Again for interpretive ease, panel B in Figure I graphs the reduced form and IV estimates
of the mathematics test score percentile premium for the oldest students (R=11) compared to the
youngest students (R=0). The results are similar to those shown in panel A in the sense that
countries with lower failure rates tend to have larger relative age effects (one exception is
Portugal), the difference between the reduced form and IV estimates are largest in countries with
high failure rates, and New Zealand is again an outlier. The main difference between the fourth
and eighth grade estimates is the magnitude of the relative age effect. While the test score
premium enjoyed by the relatively oldest students falls in all countries, it remains economically
important at the eighth grade level in almost all countries. The oldest students continue to score
4 or more percentiles higher than the youngest students (based on the reduced form) in fourteen
of the nineteen countries.
Overall, the results presented in Table IV point to the persistence of sizeable relative age
effects into adolescence across almost all countries. This finding is important because it shows
20
that early relative age effects are propagated by a wide range of educational structures: From the
Japanese system of automatic promotion, to the accomplishment oriented French system, to the
supposedly more flexible skill-based program models used in Canada and the United States.
The results reported above also speak to the question of whether relative age, birth date
combined with school starting and stopping rules, is a legitimate instrument for education in
adult outcome regressions (i.e. wages, employment, or even offspring health). An identification
strategy of this type requires that there is no direct association between birth date and the
outcome of interest (see Angrist and Krueger [1991] or Bound, Jaeger, and Baker [1995]). In
contrast to this requirement, the results presented in this paper indicate that relative age has a
direct impact on test scores as late as the end of middle school or early high school, as well as on
college enrollment. In subsequent work, Dhuey and Lipscomb [2005] also show that relatively
old children are more likely to be leaders in high school, which has in turn been shown to
increase wages in adulthood [Kuhn and Weinberger 2005]. As such, relative age appears to have
a direct effect on human capital accumulation holding educational attainment constant and is
therefore likely to have a direct impact on adult outcomes such as wages, independent of its
effect through educational attainment. While the age effects listed above should bias IV
estimates of the return to education downward it is certainly possible that there are other existing
age effects working in the opposite direction. Further complicating matters is the fact that the
relationship between relative age and educational attainment is non-monotonic. While older
students may be more likely to drop out of high school because they reach the compulsory school
age at lower levels of educational attainment, older students are also more likely to attend
academic universities (see Section VI).
21
V.C. Potential Season of Birth Effects
Although the fact that school starting rules differ across countries gives us substantial
confidence that we are not confounding relative age effects with season of birth effects, in this
section we take advantage of the cross-national dimension of TIMSS to control for season of
birth effects directly by estimating an alternative specification that includes both assigned
relative age and month of birth using data pooled across countries with cut-off dates in different
months (equation (4)).16 The results are reported in Table V. In all cases, the reported
coefficients are for relative age (RF and FS) or observed age (OLS and IV). In addition, the set
of controls (X) listed in Section IV are included in all models. For comparative purposes, row A
reports a base model that includes only relative age and country indicators. The point estimates
in this row reflect the average reduced form and IV estimates across the entire international
sample with no controls for season of birth. In all cases, these estimates are about what one
would have guessed by averaging the country specific estimates reported in Tables III and IV.
In order to control for season of birth effects, row B further includes a vector of birth
month indicators. A comparison of rows A and B reveals that both the reduced form and IV
estimates are remarkably robust to the inclusion of season of birth. The point estimates reported
in rows A and B are very close in all cases. Referring to IV estimates reported in column 4, one
month of additional relative age increases the average math test score by 0.243, which translates
into an average math test score premium for the relatively oldest (R=11) compared to the
relatively youngest (R=0) of 2.7 points on an internationally standardized test with a mean of 50
and a standard deviation of 10.
Finally, row C further adds the age at which each child is eligible for school entry to the
list of controls. This variable is calculated using the school entry age and cut-off dates reported
22
in Appendix Table I combined with month of birth. This variable captures the absolute age at
which children are eligible to enter school, which differs across birth dates and countries. It is
important to separate absolute and relative age if, for example, human capital accumulation rates
depend on age. Since there is no theoretical reason to impose any particular functional form on
absolute age, it enters the row C specification as unconstrained months of absolute age
indicators. While the point estimates in row C are slightly smaller compared to the specification
that includes relative age and month of birth but not absolute age at school eligibility (row B),
the differences are never statistically significant.
VI. THE IMPACT OF RELATIVE AGE ON PRE-UNIVERSITY BEHAVIOR
IN THE UNITED STATES AND BRITISH COLUMBIA
The strength of the relative age effects estimated across a wide range of countries at the
fourth and eighth grade levels lead one to wonder how far these effects propagate themselves
forward. In fact, the continuing strength of relative age in the eighth grade sample, when most
children are thirteen or fourteen years of age, suggests that relative age may play a role in
determining educational success throughout the educational process – even into college.
Unfortunately, it is difficult to find data sources that contain completed education and birth dates.
One exception is the 1980 United States Census, which reports quarter of birth. However, it is
difficult to analyze the long run relative age effects during the eras covered by this data because
they are confounded by the large fraction of students dropping out immediately upon reaching
the school leaving age as well as by the G.I. Bills instituted after World War II and the Korean
War. We are, however, aware of two recent studies examining the impact relative age and
educational attainment. Consistent with the estimates discussed in the next two sub-sections,
23
both Fredriksson and Öckert [2004] and Puhani and Weber [2005] find that relatively old
students attain higher levels of education in Sweden and Germany, respectively.
Although we do not have representative micro data that include birth dates and higher
education choices for all of the countries included in the analysis so far, we have obtained microlevel data that includes birth dates and pre-university choices for the Canadian province of
British Columbia and data on birth dates, pre-university choices, and university enrollment for
the United States. The British Columbia data is a comprehensive restricted-use administrative
data set including every student enrolled in a public school on an annual basis compiled by the
Ministry of Education and maintained by Edudata Canada at the University of British Columbia.
The United States data comes from the second and third waves of the restricted-use version of
NELS data discussed earlier in the paper.
VI.A. Pre-University Behavior in British Columbia
The best available data on pre-university academic behavior during the final years of high
school comes from British Columbia, Canada. The Ministry of Education tracks student
enrollment by grade each October. We therefore have panel data reporting each student’s grade
level as of October for a nine-year period (1995-2003). In addition, we also know each student’s
birth date, sex, and school of enrollment in each year that they are enrolled.17 Moreover, since
these data include all students enrolled in the British Columbia education system, non-random
selection is not a concern. Further, since all Canadian provinces have a January 1 cut-off date,
we can be quite confident that we have correctly measured relative age in almost all cases.18
However, as this is administrative data and not a panel survey, we have no information for
students who leave the British Columbia school system, either because they move to a different
province or because they drop out of school. This does not cause a problem as long as the
24
probability that a youth leaves the British Columbia school system because they move to another
province is independent of their birth month.19
Unfortunately, given the structure of the available data, we cannot track individual
students over their entire public school career. We can, however, track individuals who entered
grade nine for the first time from 1996-1998 for five years; this allows one extra year to finish
high school so that we do not misclassify students who take an extra year complete high school.
We restrict the sample to students observed in grade nine to avoid non-random sampling. Under
this sampling strategy, we have the universe of students who enter grade nine regardless of
whether or not they finish high school.20 This is particularly important because it is possible that
relative age affects high school dropout behavior.
We then define students as “university-bound” if we observe them in grade 12 during the
appropriate sample period, if they report having graduated by June of the fifth year after they
enter grade nine and have taken at least four examinable subjects and earned a 75 percent
average or higher.21 It is important to point out that this definition reflects the fact that we are
interested in identifying highly successful students who are bound for purely academic
institutions of higher learning rather than vocational or lower-end academic programs. Guided
by this objective, the aforementioned “university-bound” definitions capture two important
features of the British Columbia education system. First, most academic, or pre-university,
courses require students to take a province-wide final examination that is written and graded by
the Ministry of Education. During the period of interest, the grade on these exams constituted 40
percent of the final grade for these courses, with the other 60 percent being assigned at the
school-level by teachers. Secondly, in order to gain admission into one of the flagship provincial
universities students must generally take at least four examinable subjects and score in excess of
25
75 percent – this is just an approximation, not a formal rule set out by the universities. As a
sensitivity check, we also alternatively define an individual as university-bound if they if we
observe them in grade 12 during the appropriate sample period, they report having graduated by
June of the fifth year after they enter grade nine, they take at least four examinable subjects, and
they earn a 75 percent or higher average across all attempted provincial exams, rather than 75
percent across examinable courses.
Since we have few control variables, but can identify schools, we estimate the model
using school fixed effects. The reduced form is given by:
(5) Csyi = ψ 1s + ψ 2 y + ψ 3 Rsyi + ψ 4 Fsyi + ν syi
where ψ 1s is a vector of school fixed effects, defined by the school of record in grade nine, ψ 2 y is
a vector of ninth grade year indicators, and F is a female indicator. Following the analysis in all
previous sections, we report the OLS, first stage, reduced form, and IV estimates in Table VI.
Whenever actual age is used, it refers to the individual’s age the first time they are observed in
grade nine. In all cases, the models are estimated using a linear probability model and the
reported standard errors are heteroskedastic consistent.
Column 1 reports the fraction of students defined as university-bound, and columns 2-5
report the OLS, first stage, reduced form, and IV estimates for relative age. Based on our
primary definition of “university-bound,” 18 percent of British Columbia students are defined as
university-bound. To give the reader some perspective, the university participation rate among
18-21 year olds in British Columbia was 13.3 percent in 2002/2003.22 More importantly, the
reduced form estimates reported in column (3) reveal that the relatively oldest students are 1.8
percentage points, or 9.8 percent, more likely to be university-bound than the relatively
26
youngest. As one would expect, the IV estimates are somewhat larger – the relatively oldest are
12.8 percent more likely to be university-bound than the relatively youngest.
VI.B. Pre-University and University Enrollment Behavior in the United States
To examine pre-university and university enrollment behavior in the United States, we
return to the restricted-use NELS data discussed earlier in the paper. In contrast to the eighth
grade results, which are based on the first wave of the survey, in this section we use the second
and third waves conducted in 1992 and 1994, respectively. While the waves are different, the
sample exclusions and the control variables are identical to those described in Section IV.C.23
The second wave of NELS was conducted in 1992 while the respondents were in grade
twelve. As we are interested in the impact of relative age on “academic” success, we are
consequently interested in separating all college going, including vocational and/or quasiacademic programs, from high-level academic degree pursuits. The most obvious indicator of
such aspirations reported in the second wave of NELS is whether the respondent has taken the
SAT exam, ACT exam, or both. This is an appealing measure because most flagship colleges
and universities require a SAT or ACT score as part of their application process. In a similar
vein, data from the third wave of NELS, conducted in 1994, almost two years after the on-time
high school graduation date, reports whether respondents have enrolled in a four-year accredited
college/university during the previous two years. Again, this is an appealing measure because it
isolates academic post-secondary enrollment.
The results for the same set of models reported for British Columbia are also reported for
the United States university measures in rows 3 and 4 in Table VI. Column 1 reports the fraction
of students designated as belonging to the group of interest (having taken the SAT or ACT or
enrolling in an accredited four-year postsecondary institution), and columns 2-5 report the OLS,
27
first stage, reduced form, and IV estimates for relative age. The reduced form estimates reported
in column (3) reveal that the relatively oldest students are 4.6 percentage points, or 7.7 percent
more likely to have taken the SAT or ACT, and 4.6 percentage points, or 11.6 percent, more
likely to enroll in an accredited four-year college/university. In addition, as one would expect,
the IV estimates are somewhat larger – the relatively oldest are 11.1 (10.7) percentage points
more likely to have taken the SAT or ACT (enrolled in college) than the relatively youngest.
VII. CONCLUSION
The large relative age effects reported in this paper are the result of what many might
consider a necessary and benign educational construct: a single school starting date. Despite the
theoretical possibility of long-run relative age effects, one might have expected these effects to
exist early in the educational process, but then dissipate with age, making the single start date
seem both easy and innocuous. However, the results reported in this paper cast serious doubt on
this view. In particular, we find that the oldest students score 4-12 percentiles higher than the
youngest students at the fourth grade level and 2-9 percentiles higher at the eighth grade level
across a wide range of countries. The TIMSS results are corroborated by the fact that relatively
older students in British Columbia and the United States are more likely to participate in preuniversity academic programs during the final years of high school, and more likely to enter a
flagship postsecondary institution in the United States. Further, the findings reported in this
paper are consistent with recent work by Heckman and various coauthors (see Cuhna, Heckman,
Lochner, and Masterov [2006]) showing that over the childhood lifecycle skills beget skills
through a multiplier process: Skills accumulated early in childhood are complementary to later
learning.
28
The fact that early advantages held by relatively old children persist into adulthood
through differences in skill accumulation, college preparation, and the accumulation of softer
skills, such as leadership (see Dhuey and Lipscomb [2005]), suggests that we should pay close
attention to early school structures that affect skill acquisition. For example, we should learn
more about the long-run differences in educational outcomes in countries with no, or at least
limited, ability differentiated learning groups during the primary grades like Denmark and
Finland [OFSTED 2003], compared to countries where children are separated into abilityspecific curriculum groups during the early primary grades, such as England and the United
States [Mullis et al. 2002 and 2003].
The finding of long-run relative age effects also has potentially important implications for
the distribution of skills across socioeconomic groups in countries that allow parents to defer
school entry. In the United States, for example, 5 percent of children enter kindergarten a year
later than they are eligible to do so. While this may seem innocent enough, 77 percent of
deferrals are for students born in the last relative quarter, and 30 percent of these children are
from the top quarter of the socioeconomic distribution. As such, low socioeconomic children
now make up a disproportionately large share of the relatively youngest quarter, which is a cause
for concern, since these children are now at two substantial disadvantages.
Department of Economics, University of California at Santa Barbara
Department of Economics, University of California at Santa Barbara
29
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School Starting Age on School and Labor Market Performance,” Working Paper, (2004).
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(2004), 226-244.
30
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(Boston, MA: International Study Center-Boston College, 2002).
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International Mathematics Report: Findings from IEA’s Trends in International
Mathematics and Science Study at the Fourth and Eighth Grades, (TIMSS and PIRLS
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Standards, Definitions and Classifications, (OECD, 2004).
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England, and Finland, an International Comparison, (OFSTED Publications Centre,
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31
1
Early performance gaps by any identifiable group, e.g. race, socioeconomic status, or gender, can similarly
propagate themselves through time via the same multiplier process.
2
England and New Zealand have multiple kindergarten entry dates, but a single first grade entry point. Although
United States states set their own cut-off dates, and hence there are many cut-off dates in the United States, in most
jurisdictions a single date applies to all residents (see Appendix Table II).
3
We thank two anonymous referees for making this suggestion.
4
There is also a large education literature on age effects (see de Cos [1997) and the references therein).
5
Both countries have an unreasonably large percentage of births occurring in January and February. The percentage
of births occurring in December, January, February, and March are: 8.3, 10.4, 10.5, and 7.9 in Korea and 5.7, 12.0,
8.0, and 8.2 in Turkey. According to colleagues from Korea it is not uncommon for parents with relatively old
children (born from March-June) to bribe officials to enter an incorrect birth date on the birth certificate so that their
child are eligible for school early. This means that some relative fourth quarter births are erroneously reclassified as
relative first quarter births. Conversely, according to colleagues from Turkey, it not uncommon for the parents of
children born in December to wait until January to register them so that they will not start school early with older
children (the reverse of the motivation in Korea).
6
In all cases, except the Italian eighth grade sample, even youth who have been retained once have not yet reached
the compulsory schooling age (see www.right-to-education.org). As youth in Italy can leave school at age fourteen,
it is possible that we have a non-random eighth grade sample for Italy. However, this possibility does not seem to
be concern since all estimates are similar if we restrict the Italian sample to seventh graders.
7
All results are similar if internationally standardized test scores are used instead.
8
The results are not specification specific. All results are similar if we exclude observations with missing data or if
we include all observations but only sex, grade, and test year indicators, or no covariates at all.
9
Cascio and Lewis [2006] isolate the impact of an additional year of schooling on AFQT scores using NLSY data.
10
States are excluded if they change school start dates during the period of interest, list their cut-off date as the start
of the school year because we do not have a complete historical listing of school start dates, or allow local education
authorities to set their own cut-off date (see Appendix Table II).
11
The fraction of mothers in the more and less educated groups is not always evenly split because TIMSS reports
maternal education in six categories, and in some cases a single category includes a large percentage of mothers.
More detail is available in the working paper version of the paper.
12
One potential concern with Table II is that the small sample sizes in TIMSS (2,920 to 25,063) might make it
difficult to detect small differences in birth patterns across maternal education groups. We therefore repeated the
analysis using the United States Natality Detail Files for 1997-1999 and find similar results. (These results are
available in the working paper version of the paper.)
13
See the working version of the paper for a detailed analysis of the impact of relative age on retention and
acceleration.
14
These results are consistent with the finding of Jacob and Lefgren [2004] that retention in Chicago public schools
successfully increases third grade test scores. Further consistent with Jacob and Lefgren [2004], we will see in
Section V.B, that in contrast to the fourth grade results, we can rarely reject that the IV and reduced form results are
statistically different at the eighth grade level – Jacob and Lefgren [2004] similarly find that sixth grade test scores
are not increased by retention. Given these results, it seems safe to say that in the short run primary grade retention
increases student achievement, but that the long run impact is much less clear.
15
The results for specifications including non-linear relative measures and male-female sub-samples are available in
the working paper version of the paper.
16
New Zealand is excluded from the cross-country analysis due to the reversal of seasons in the southern
hemisphere. However, all results are similar if New Zealand is included, and are available upon request. The
United States is excluded because the data do not come from the TIMSS sample.
17
Both the student and school identifiers included in the data are encoded to ensure confidentiality. Further, due to
confidentiality concerns, Aboriginal and ESL students were removed from the data before we received it.
18
The only exception is foreign born students who enter the British Columbia education system prior to grade nine,
but as we exclude ESL students, this only leaves English speaking foreign born students who entered the British
Columbia education system between kindergarten and grade nine, which is a small number.
19
However, we make no such assumption regarding the probability that a student drops out of high school; recent
studies by Angrist and Krueger [1991] Cascio and Lewis [2006] and McCrary and Royer [2005] show that
educational attainment and particularly dropping out are a function of birth month due to school entry age cut-offs.
32
20
There are, however, two sample exclusions. First, students who report a disability in any year are excluded from
the data. Second, the sample is restricted to students attending schools with ten or more students enrolled in grade
nine between 1996-1998. The second restriction is imposed to allow the inclusion of school fixed effects, however,
all results are similar in the absence of this restriction and with the exclusion of fixed effects and are available upon
request.
21
We use the highest exam and course grades reported for the small fraction of students who attempt a course more
than once.
22
See http://www.millenniumscholarships.ca/en/research/pokbc.asp for more detail.
23
The only additional sample restriction is that we exclude students who attend a school with fewer than ten
students to allow for the use of fixed effects.
33
Table I
Summary Statistics
Fourth Grade
Austria
Math
(1)
Science
(2)
52.35
52.57
(9.27)
(8.55)
Eighth Grade
Relative Age Observed Age Sample
(3)
(4)
(5)
5.38
(3.45)
119.61
(8.50)
5,045
Belgium
Math
(6)
Science
(7)
52.69
53.28
55.21
51.27
(8.85)
(8.45)
Canada
50.23
51.36
Czech Republic
53.18
51.80
(9.20)
(8.81)
5.58
114.61
15,588
52.69
52.26
5.44
119.00
6,523
54.30
54.52
49.07
46.68
50.21
53.25
Finland
53.96
54.07
France
51.90
47.76
(9.30)
(9.31)
(8.89)
(8.53)
(3.41)
(3.44)
(9.00)
(8.11)
Denmark
England
(8.57)
(8.65)
(8.51)
47.88
(9.76)
51.29
(9.78)
5.54
(3.45)
114.53
(6.90)
6,066
(9.25)
(7.33)
(8.09)
Greece
46.48
47.25
Iceland
44.32
46.16
(9.92)
(8.70)
(8.95)
(9.07)
53.87
New Zealand
47.22
49.76
Norway
46.37
48.69
Portugal
45.51
45.57
(8.94)
(9.65)
(7.94)
(8.31)
109.53
5,952
46.93
47.67
5.43
109.50
3,431
48.00
48.03
49.31
49.99
(3.36)
(7.46)
(6.92)
(9.10)
(7.97)
(9.06)
55.44
(8.15)
5.80
(3.40)
Italy
Japan
(8.89)
(9.03)
(8.44)
(8.77)
5.60
118.70
8,536
58.00
54.60
5.43
113.93
4,916
50.14
50.99
5.60
112.17
4,300
48.80
50.55
5.45
117.26
5,451
44.59
46.04
Slovak Republic
53.83
52.64
Spain
47.48
49.95
Sweden
52.05
52.68
--
--
United States*
(8.03)
(9.70)
(9.10)
(9.28)
(7.43)
(9.78)
(9.65)
(9.55)
(3.41)
(3.47)
(3.37)
(3.42)
(6.89)
(7.27)
(7.14)
(12.92)
(8.15)
(9.13)
(8.56)
(7.10)
(8.69)
(8.07)
(8.97)
--
--
5.90
(3.56)
102.59
(4.09)
6,091
(8.31)
(9.42)
(8.82)
(8.21)
(8.36)
(8.32)
(9.16)
Relative Age Observed Age Sample
(8)
(9)
(10)
5.42
165.63
5,528
5.52
165.45
15,650
5.46
165.13
25,062
5.40
168.31
10,123
5.68
160.99
4,251
5.58
165.56
6,515
5.66
166.11
2,920
5.49
165.56
5,610
5.65
157.26
7,800
5.59
157.54
3,718
5.57
163.96
8,163
5.58
168.51
14,889
5.43
168.27
10,476
5.74
160.25
5,644
5.47
167.56
6,600
5.42
167.04
10,597
5.49
164.99
7,595
5.75
167.21
8,823
5.36
170.19
15,155
(3.47)
(3.41)
(3.40)
(3.44)
(3.40)
(3.48)
(3.37)
(3.40)
(3.45)
(3.40)
(3.40)
(3.41)
(3.47)
(3.35)
(3.42)
(3.46)
(3.42)
(3.38)
(3.47)
(8.50)
(9.57)
(8.60)
(7.69)
(7.70)
(7.17)
(4.23)
(10.91)
(8.84)
(7.03)
(8.54)
(6.63)
(10.93)
(7.23)
(13.36)
(7.23)
(10.31)
(10.56)
(7.20)
Test scores are internationally standardized to mean 50 and standard deviation 10. Sample means are population weighted. *U.S. data are from the ECLS for grade 3 and NELS for
grade 8. All other data are from TIMSS.
Table II
Quarter of Birth Patterns
Calendar Quarter of Birth
Austria
Belgium
Canada
Czech Republic
Denmark
England
Finland
France
Greece
Iceland
Italy
Japan
New Zealand
Norway
Portugal
Slovak Republic
Spain
Sweden
School Quarter of Birth
Maternal Education Difference (More-Less)
Q1
(1)
Q2
(2)
Q3
(3)
Q4
(4)
Q1
(5)
Q2
(6)
Q3
(7)
Q4
(8)
Q1
(9)
Q2
(10)
Q3
(11)
Q4
(12)
0.250
0.244
0.244
0.257
0.256
0.246
0.251
0.237
0.229
0.240
0.248
0.239
0.244
0.249
0.238
0.254
0.241
0.265
0.250
0.263
0.258
0.260
0.273
0.250
0.273
0.268
0.266
0.261
0.268
0.247
0.254
0.283
0.257
0.255
0.257
0.268
0.257
0.253
0.256
0.255
0.244
0.254
0.256
0.254
0.268
0.261
0.246
0.271
0.247
0.246
0.259
0.263
0.254
0.252
0.244
0.241
0.243
0.229
0.227
0.251
0.220
0.241
0.237
0.238
0.237
0.244
0.255
0.222
0.246
0.228
0.248
0.215
0.262
0.241
0.243
0.254
0.227
0.241
0.220
0.241
0.241
0.238
0.237
0.239
0.256
0.222
0.246
0.255
0.248
0.215
0.247
0.253
0.256
0.266
0.244
0.257
0.256
0.254
0.250
0.261
0.246
0.244
0.246
0.246
0.259
0.259
0.254
0.252
0.251
0.263
0.258
0.242
0.273
0.245
0.273
0.268
0.267
0.261
0.268
0.271
0.257
0.283
0.257
0.245
0.257
0.268
0.241
0.244
0.244
0.238
0.256
0.257
0.251
0.237
0.242
0.240
0.248
0.247
0.241
0.249
0.238
0.240
0.241
0.265
-0.016
0.009
0.023
0.010
-0.002
0.000
-0.008
0.005
0.006
--0.008
0.007
-0.018
0.012
0.022
-0.001
-0.000
0.005
0.015
-0.040
-0.006
0.033
0.021
0.000
-0.019
-0.015
-0.019
-0.007
0.007
0.005
0.027
--0.009
0.001
-0.028
0.005
--0.025
-0.011
-0.008
-0.020
0.020
-0.001
-0.001
0.027
-0.001
0.004
-0.002
--0.007
-0.015
-0.010
0.025
-0.016
-0.022
-0.006
0.015
-0.008
--0.007
0.013
-0.002
-0.018
-0.031
-0.024
All data are pooled across grades 4 and 8 and are from TIMSS. All proportions are population weighted. The shaded values in columns 1-8 indicate the quarter with the highest
fraction of births. The bold coefficients in columns 9-12 indicate that the difference between the fraction of births to "more" educated mothers differs from the fraction of births to
"less" educated mothers at the 5 percent level or better. The results reported in columns 9-12 are based on the eighth grade sample (maternal education is not reported in the fourth
grade sample), and Austria, England, and Japan are excluded because they do not report maternal education in the eighth grade sample.
Table III
The Impact of Relative Age on Test Scores at the Fourth Grade Level
Math
OLS
(1)
Austria
Canada
Czech Republic
England
Greece
Iceland
Japan
New Zealand
Norway
Portugal
United States*
RF
(2)
Science
FS
(3)
IV
(4)
OLS
(5)
RF
(6)
FS
(7)
IV
(8)
-0.262
0.108
0.540
0.201
-0.196
0.149
0.540
0.276
(0.031)
(0.049)
(0.031)
(0.097)
(0.031)
(0.048)
(0.031)
(0.096)
0.010
0.115
0.607
0.190
-0.011
0.110
0.607
0.181
(0.018)
(0.036)
(0.025)
(0.059)
(0.019)
(0.036)
(0.025)
(0.060)
-0.200
0.111
0.498
0.223
-0.127
0.180
0.498
0.362
(0.023)
(0.034)
(0.019)
(0.069)
(0.024)
(0.034)
(0.019)
(0.070)
0.274
0.315
0.955
0.330
0.250
0.267
0.955
0.280
(0.034)
(0.036)
(0.008)
(0.038)
(0.033)
(0.036)
(0.008)
(0.038)
0.131
0.196
0.894
0.219
0.130
0.245
0.894
0.274
(0.031)
(0.040)
(0.016)
(0.044)
(0.030)
(0.040)
(0.016)
(0.045)
0.183
0.254
0.984
0.258
0.180
0.247
0.984
0.251
(0.046)
(0.050)
(0.008)
(0.051)
(0.047)
(0.050)
(0.008)
(0.051)
0.244
0.280
0.962
0.291
0.306
0.353
0.962
0.367
(0.031)
(0.031)
(0.005)
(0.032)
(0.032)
(0.031)
(0.005)
(0.032)
0.081
0.202
0.469
0.430
0.078
0.173
0.469
0.369
(0.033)
(0.039)
(0.023)
(0.086)
(0.033)
(0.040)
(0.023)
(0.086)
0.178
0.238
0.933
0.255
0.164
0.248
0.933
0.265
(0.039)
(0.041)
(0.011)
(0.044)
(0.040)
(0.042)
(0.011)
(0.046)
-0.096
0.195
0.758
0.258
-0.073
0.191
0.758
0.252
(0.012)
(0.038)
(0.042)
(0.054)
(0.013)
(0.039)
(0.042)
(0.054)
0.277
0.230
0.774
0.298
0.341
0.267
0.774
0.345
(0.038)
(0.040)
(0.016)
(0.051)
(0.034)
(0.038)
(0.016)
(0.048)
*U.S. data are from the ECLS and all other data are from TIMSS. All models are population weighted and heteroskedasticconsistent standard errors are in parentheses. Bold coefficents are significant at the 5 percent level or better. Countries with
minimal late entry, failure, or early entry are shaded. RF stands for reduced form and reports the coefficient estimate for assigned
relative age from equation (3). FS stands for first stage and reports the coefficient estimates for assigned age from equation (2). Fstatistics for the first stage range from 295-35,475. IV estimates use assigned age to instrument for observed age in equation (1).
All TIMSS models include controls for: sex, grade, rural residential locations, native born mother, native born father, child lives with
both parents, child has a calculator, child has a computer, child has more than 100 books, a continuous measure for the number of
people residing in the child’s household, and a complete set of indicators for controls with missing information. The U.S. models
using ECLS data includes controls for: sex, race, number of siblings, rural status, parental education, whether child lives with both
parents, has over 100 books, and has a calculator.
Table IV
The Impact of Relative Age on Test Scores at the Eighth Grade Level
Math
OLS
(1)
Austria
Belgium
Canada
Czech Republic
Denmark
England
Finland
France
Greece
Iceland
Italy
Japan
New Zealand
Norway
Portugal
Slovak Republic
Spain
Sweden
United States*
RF
(2)
Science
FS
(3)
IV
(4)
OLS
(5)
RF
(6)
FS
(7)
IV
(8)
-0.227
0.099
0.617
0.160
-0.172
0.115
0.617
0.186
(0.024)
(0.040)
(0.024)
(0.066)
(0.025)
(0.039)
(0.024)
(0.065)
-0.379
0.097
0.719
0.134
-0.218
0.123
0.719
0.171
(0.015)
(0.031)
(0.021)
(0.045)
(0.015)
(0.030)
(0.021)
(0.043)
-0.060
0.082
0.509
0.162
-0.127
0.097
0.509
0.190
(0.014)
(0.026)
(0.020)
(0.052)
(0.015)
(0.026)
(0.020)
(0.051)
-0.299
0.077
0.560
0.137
-0.209
0.108
0.560
0.193
(0.021)
(0.033)
(0.017)
(0.060)
(0.022)
(0.033)
(0.017)
(0.059)
-0.200
0.011
0.559
0.020
-0.158
0.027
0.559
0.049
(0.036)
(0.045)
(0.025)
(0.080)
(0.035)
(0.045)
(0.025)
(0.080)
0.068
0.166
0.951
0.175
0.091
0.159
0.951
0.167
(0.031)
(0.034)
(0.010)
(0.036)
(0.031)
(0.034)
(0.010)
(0.036)
-0.130
0.049
0.918
0.054
-0.059
0.106
0.918
0.115
(0.045)
(0.057)
(0.019)
(0.062)
(0.047)
(0.056)
(0.019)
(0.061)
-0.298
0.075
0.599
0.125
-0.192
0.093
0.599
0.155
(0.015)
(0.038)
(0.038)
(0.066)
(0.015)
(0.038)
(0.038)
(0.067)
-0.109
0.170
0.795
0.214
-0.087
0.163
0.795
0.206
(0.016)
(0.030)
(0.020)
(0.039)
(0.017)
(0.030)
(0.020)
(0.039)
-0.013
0.092
0.959
0.096
0.063
0.179
0.959
0.187
(0.047)
(0.052)
(0.016)
(0.055)
(0.047)
(0.054)
(0.016)
(0.056)
-0.147
0.101
0.792
0.128
-0.125
0.117
0.792
0.148
(0.016)
(0.031)
(0.021)
(0.040)
(0.018)
(0.031)
(0.021)
(0.040)
0.228
0.234
0.983
0.238
0.226
0.235
0.983
0.239
(0.024)
(0.024)
(0.003)
(0.025)
(0.023)
(0.024)
(0.003)
(0.024)
-0.166
0.138
0.391
0.353
-0.161
0.149
0.391
0.380
(0.022)
(0.027)
(0.016)
(0.072)
(0.021)
(0.026)
(0.016)
(0.071)
0.056
0.200
0.847
0.236
0.095
0.228
0.847
0.269
(0.036)
(0.041)
(0.014)
(0.048)
(0.036)
(0.039)
(0.014)
(0.046)
-0.204
0.146
0.588
0.248
-0.164
0.142
0.588
0.241
(0.009)
(0.034)
(0.043)
(0.065)
(0.010)
(0.034)
(0.043)
(0.064)
-0.182
0.179
0.804
0.222
-0.163
0.144
0.804
0.179
(0.022)
(0.028)
(0.012)
(0.035)
(0.022)
(0.028)
(0.012)
(0.035)
-0.262
0.159
0.766
0.207
-0.207
0.144
0.766
0.188
(0.012)
(0.033)
(0.028)
(0.045)
(0.014)
(0.032)
(0.028)
(0.044)
-0.033
0.155
0.921
0.168
-0.010
0.163
0.921
0.177
(0.028)
(0.030)
(0.009)
(0.033)
(0.027)
(0.030)
(0.009)
(0.033)
-0.257
0.103
0.438
0.235
-0.187
0.098
0.438
0.223
(0.011)
(0.024)
(0.019)
(0.057)
(0.011)
(0.024)
(0.019)
(0.057)
*U.S. data are from the NELS and all other data are from TIMSS. All models are population weighted and heteroskedasticconsistent standard errors are in parentheses. Bold coefficents are significant at the 5 percent level or better. Countries with
minimal late entry, failure, or early entry are shaded. RF stands for reduced form and reports the coefficient estimate for assigned
relative age from equation (3). FS stands for first stage and reports the coefficient estimates for assigned age from equation (2). Fstatistics for the first stage range from 189-125,577. IV estimates use assigned age to instrument for observed age in equation (1).
All TIMSS models include controls for: sex, grade, test year, rural residential locations, native born mother, native born father,
child lives with both parents, maternal education, child has a calculator, child has a computer, child has more than 100 books, a
continuous measure for the number of people residing in the child’s household, and a complete set of indicators for controls with
missing information. The U.S. models using NELS data includes controls for: sex, race, family size, living with both parents, urban,
has over 50 books, has a calculator, and parental education.
Table V
The Impact of Relative Age on Test Scores - Pooled Country Sample
Math
OLS
(1)
RF
(2)
Science
FS
(3)
IV
(4)
OLS
(5)
RF
(6)
FS
(7)
IV
(8)
Grade 4, Additional Variables:
(A) None
(B) Month of Birth
(C) Month of Birth and Eligible School Entry Age
0.053
0.213
0.869
0.245
0.066
0.228
0.869
0.263
(0.010)
(0.015)
(0.005)
(0.018)
(0.010)
(0.014)
(0.005)
(0.017)
0.036
0.209
0.859
0.243
0.046
0.217
0.859
0.253
(0.010)
(0.016)
(0.006)
(0.018)
(0.010)
(0.015)
(0.006)
(0.018)
-0.071
0.203
0.829
0.245
-0.062
0.198
0.829
0.239
(0.010)
(0.029)
(0.013)
(0.035)
(0.010)
(0.027)
(0.013)
(0.032)
Grade 8, Additional Variables:
(A) None
(B) Month of Birth
(C) Month of Birth and Eligible School Entry Age
-0.122
0.133
0.814
0.163
-0.089
0.129
0.814
0.159
(0.005)
(0.009)
(0.006)
(0.012)
(0.005)
(0.010)
(0.006)
(0.012)
-0.135
0.132
0.836
0.158
-0.103
0.120
0.836
0.144
(0.005)
(0.011)
(0.006)
(0.013)
(0.005)
(0.011)
(0.006)
(0.014)
-0.207
0.128
0.867
0.147
-0.163
0.132
0.867
0.152
(0.006)
(0.020)
(0.008)
(0.023)
(0.006)
(0.020)
(0.008)
(0.024)
All data are from TIMSS. All models are population weighted and heteroskedastic-consistent standard errors are in parentheses. Bold coefficents are significant at
the 5 percent level or better. RF stands for reduced form and reports the coefficient estimate for assigned relative age. FS stands for first stage and reports the
coefficient estimates for assigned age. F-statistics for the first stage range from 4,084-27,701. IV estimates use assigned age to instrument for observed age. All
models include controls for: sex, grade (for eighth grade models only), test year, rural residential locations, native born mother, native born father, child lives with
both parents, maternal education (for eighth grade models only), child has a calculator, child has a computer, child has more than 100 books, a continuous
measure for the number of people residing in the child’s household, and a complete set of indicators for controls with missing information.
Table VI
The Impact of Relative Age on College Preparation
Mean
(1)
OLS
(2)
RF
(3)
FS
(4)
IV
(5)
Sample Size
(6)
British Columbia
75%+ in Examinable Courses*
75%+ Across All Exams
0.18
-0.0032
0.0016
0.7570
0.0021
[0.39]
(0.0004)
(0.0003)
(0.0051)
(0.0004)
0.16
-0.0030
0.0013
0.7570
0.0018
[0.37]
(0.0004)
(0.0003)
(0.0051)
(0.0004)
106,917
106,917
United States
Took SAT or ACT
Enrolled in a 4-year Accredited College
0.60
-0.0114
0.0042
0.4181
0.0101
[0.49]
(0.0010)
(0.0016)
(0.0247)
(0.0040)
0.40
-0.0090
0.0042
0.4325
0.0097
[0.49]
(0.0008)
(0.0017)
(0.0264)
(0.0041)
10,200
7,644
*75% average across all examinable courses taken. The B.C. data are restricted-use administrative data provided by the B.C.
Ministry of Education and the U.S. data are from NELS. Heteroskedastic-consistent standard errors are in parentheses. Standard
deviations in square parentheses. Bold coefficents are significant at the 5 percent level or better. RF stands for reduced form and
reports the coefficient estimate for assigned relative age. FS stands for first stage and reports the coefficient estimates for assigned
age. F-statistics for the first stage range from 269-21,880. IV estimates use assigned age to instrument for observed age in grade
nine (eight) in British Columbia (the United States). All B.C. models inlcude school fixed effects, year indicators, and a female dummy
variable. All U.S. models are population wieghted and include school fixed effects as well as controls for: sex, race, family size, living
with both parents, owning more than 50 books, owning a calculator, and parental education.
Appendix Table I
Differences in International Educational Systems
Percent
Percent
Age at End of
Percent
Percent
Compulsory Behind as of Ahead as of Behind as of Ahead as of
Grade 3/4
Grade 7/8
Grade 7/8
Education
Grade 3/4
School Cutoff Date
Age at
School
Entry
Austria
January 1
6
yes
8
17
15
Belgium-Flemish
January 1
6
yes
8
38
Belgium-French
January 1
6
yes
6
Canada
January 1
5-6
yes
Czech Republic
Ability Grouping First Grade
Percent
in Primary
with Formal Academic at
School
Streaming
Grade 10
17.9
2.6
18.1
1.8
18
24.3
1.3
53
18
24.3
1.3
11
100
16-18
15.0
2.7
19.5
1.5
18.2
0.6
17.5
0.3
9.4
4.3
1.1
1.0
September 1
6
yes
9
19
15
Denmark
January 1
6
no
10
48
15
England
September 1
5
yes
9
--
16
Finland
January 1
7
no
9
43
16
4.1
0.8
France
January 1
6
yes
9
48
16
37.0
3.7
1.1
0.9
Greece
April 1
6
yes
9
61
16
4.3
0.9
12.6
1.1
Iceland
January 1
6
yes
10
37
16
0.8
0.5
0.6
1.0
Italy
January 1
6
yes
8
33
14
11.6
5.0
Japan
April 1
6
no
9
75
15
0.5
0.6
0.3
0.3
New Zealand
May 1
5
yes
11
100
16
7.2
5.0
9.1
5.9
Norway
January 1
6
yes
10
31
16
1.0
0.9
2.1
1.9
Portugal
January 1
6
--
6
71
15
21.7
0.4
37.8
0.5
September 1
6
yes
9
46
16
6.1
0.9
Spain
January 1
6
yes
8
65
16
27.5
0.3
Sweden
January 1
7
yes
9
87
16
3.1
0.7
Appendix 2
5
yes
none
100
16-18
25.3
3.1
Slovak Republic
United States
12.2
0.3
Age at school entry (age at ISCED 1 entry), first grade with formal streaming, and percent academic at grade 10 data from OECD (2004). Age at end of compulsory education is from right-toeducation.org. Ability grouping data from Arnove and Zimmerman (1999), Mullis et al. (2002 and 2003), OFSTED (2003), Stevenson and Stigler (1992), and www.eurydice.org. First grade with
formal streaming indicates the first grade in which explicit vocational tracks are offered. Percent academic at grade 10 is the percentage of students enrolled in an academic track. Percent behind
and ahead as of grade 3/4 and 7/8 are calculated from TIMSS for all countries except the U.S. which are from the ECLS for grade 3 and NELS for grade 8.
Appendix Table II
United States School Cut-off Dates
School Cut-off Date
AL
AK
AZ
AR
CA
CO
CT
DE
FL
GA
HI
ID
IL
IN
IA
KS
KY
LA
ME
MD
MA
MI
MN
MS
October 1
November 1
January 1 (≤1978)
December 1 (=1979)
November 1 (=1980)
October 1 (=1981)
September 1 (≥1982)
October 1
December 1
LEA
January 1
January 1
February 1
January 1
January 1
October 15
December 1
LEA
October 15 (≤1978)
September 15 (≥1979)
September 1
January 1 (≤1978)
October 1 (≥1979)
January 1
October 15
unknown
LEA
December 1
September 1
January 1 (≤1976)
December 1 (=1977)
November 1 (=1978)
October 1 (=1979)
September 1 (≥1980)
School Cut-off Date
MO
MT
NE
NV
NH
NJ
NM
NY
NC
ND
OH
OK
OR
PA
RI
SC
SD
TN
TX
UT
VT
VA
WA
WV
WI
WY
October 1
September 15
October 15
October 1
October 1
LEA
September 1
December 1
October 15
November 1 (≤1977)
October 1 (≥1978)
October 1
November 1
November 15
February 1
January 1
November 1
November 1 (≤1978)
September 1 (≥1979)
November 1
September 1
SSY
January 1
October 1
LEA
November 1
December 1 (≤1976)
September 1 (≥1977)
September 15
Cut-offs change dates are defined as the school year in which the change went into effect. LEA denotes
Local Eduation Authority. SSY denotes start of school year. All dates are from U.S. state statutes.
lgi
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18
Figure I.
Percentile Advantage of Oldest Versus Youngest
Panel A. Grade 4 Math
16
14
12
10
8
6
RF
IV
4
2
0
Panel B. Grade 8 Math
18
16
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10
8
6
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IV
4
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0